Probability Interior Angles are Positive IntegersDate: 09/19/2001 at 17:34:12 From: Guili Subject: Probability My question is: Find the probability that the measure of an interior angle of a regular n-gon is a positive integer if n is an integer and 3<n<12. Could you please explain? Thank you very much. Guili Date: 09/19/2001 at 17:47:33 From: Doctor Anthony Subject: Re: Probability n=3 interior angle = 60 (180 - 360/3) n=4 " " = 90 (180 - 360/4) n=5 " " = 108 (180 - 360/5) and so on Clearly, the internal angle is an integer provided 360/n = integer. 360/6 = 60 (integer) 360/7 not an integer 360/8 = 45 (integer) 360/9 = 40 (integer) 360/10 =36 (integer) 360/11 not an integer 360/12 =30 (integer) So, excluding 3 and 12, the internal angle will be an integer for n = 4, 5, 6, 8, 9, 10 (6 out of 8 occasions) So the probability that the angle is an integer = 6/8 = 3/4. - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ Date: 09/19/2001 at 21:58:15 From: Guili Subject: Re: Probability Thank you very much for your help. I appreciate it. Now, thanks to you, I understand the problem. |
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